Question

(2/3 y+5/8x+1/4)+(1/4x+1/2)

Answer 1

`\Big((2)/(3)y+(5)/(8)x+(1)/(4)\Big)+\Big((1)/(4)x+(1)/(2)\Big)`

Remove the parenthesis (this is ok since it's just all addition)

`=(2)/(3)y+(5)/(8)x+(1)/(4)+(1)/(4)x+(1)/(2)`

Now, we're going to change some of the fractions to make it possible to add them:

• 1/4 is the same thing as 2/8 (multiply both numerator and denominator by 2)
• 1/2 is the same thing as 2/4 (multiply both numerator and denominator by 2)

`=(2)/(3)y+(5)/(8)x+(1)/(4)+(2)/(8)x+(2)/(4)`

Add like terms now that the fractions are compatible

`=(2)/(3)y+(7)/(8)x+(3)/(4)`

Let me know if you need any clarifications, thanks!

~ Padoru